Apropos of anything else, CF is (reasonably) requiring a court order to remove offending material rather than just "well, company said so, so eh, just do as they say". La Liga complains that "oh, that's too slow for what we want" and just got a blanket ruling.
I am not a fan of CF but your argument seems to be "CF should just roll over any time someone says "hey, delete this", because, obviously, everyone knows it's problematic, right? Right?".
CloudFlare uses legal chicanery to try to subvert the DMCA by claiming that because they’re not the origin server, they’re not subject to takedown demands. So far no court has told them to knock it off. I expect that day will eventually come. Every lawsuit against them to date has ended in a settlement because CloudFlare would rather pay up than get an unfavorable ruling on the books.
CloudFlare has consistently treated loss of DMCA safe harbor protection as a material business risk; it’s been cited in every SEC filing from the 2019 IPO S-1 through the FY2025 10-K.